Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 12, Problem 1CQ
(a)
To determine
The phase constant in equation
(b)
To determine
The position of the particle at
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
(a) If the coordinate of a particle varies as x = -A cos wt, what is the phase constant in equation x(t) = A cos(wt + ¢)? (Use any variable or symbol stated above along with
the following as necessary: Tn.)
(b) At what position is the particle at t = 0? (Use any variable or symbol stated above along with the following as necessary: 1.)
X =
Ex. 16 : A particle performing S.H.M. has a
velocity of 10 m/s, when it crosses the mean
position. If the amplitude of oscillation is 2 m,
find the velocity when it is midway between
mean and extreme position.
A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h.
a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u.
b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.
Chapter 12 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 12.1 - A block on the end of a spring is pulled to...Ch. 12.2 - Consider a graphical representation (Fig. 12.3) of...Ch. 12.2 - Figure 12.4 shows two curves representing...Ch. 12.2 - An object of mass m is hung from a spring and set...Ch. 12.4 - A grandfather clock depends on the period of a...Ch. 12.5 - Prob. 12.6QQCh. 12 - Which of the following statements is not true...Ch. 12 - Prob. 2OQCh. 12 - Prob. 3OQCh. 12 - Prob. 4OQ
Ch. 12 - Prob. 5OQCh. 12 - Prob. 6OQCh. 12 - If a simple pendulum oscillates with small...Ch. 12 - Prob. 8OQCh. 12 - Prob. 9OQCh. 12 - Prob. 10OQCh. 12 - Prob. 11OQCh. 12 - Prob. 12OQCh. 12 - Prob. 13OQCh. 12 - You attach a block to the bottom end of a spring...Ch. 12 - Prob. 15OQCh. 12 - Prob. 1CQCh. 12 - The equations listed in Table 2.2 give position as...Ch. 12 - Prob. 3CQCh. 12 - Prob. 4CQCh. 12 - Prob. 5CQCh. 12 - Prob. 6CQCh. 12 - The mechanical energy of an undamped blockspring...Ch. 12 - Prob. 8CQCh. 12 - Prob. 9CQCh. 12 - Prob. 10CQCh. 12 - Prob. 11CQCh. 12 - Prob. 12CQCh. 12 - Consider the simplified single-piston engine in...Ch. 12 - A 0.60-kg block attached to a spring with force...Ch. 12 - When a 4.25-kg object is placed on top of a...Ch. 12 - The position of a particle is given by the...Ch. 12 - You attach an object to the bottom end of a...Ch. 12 - A 7.00-kg object is hung from the bottom end of a...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9PCh. 12 - A 1.00-kg glider attached to a spring with a force...Ch. 12 - Prob. 11PCh. 12 - Prob. 12PCh. 12 - A 500-kg object attached to a spring with a force...Ch. 12 - In an engine, a piston oscillates with simple...Ch. 12 - A vibration sensor, used in testing a washing...Ch. 12 - A blockspring system oscillates with an amplitude...Ch. 12 - A block of unknown mass is attached to a spring...Ch. 12 - Prob. 18PCh. 12 - Prob. 19PCh. 12 - A 200-g block is attached to a horizontal spring...Ch. 12 - A 50.0-g object connected to a spring with a force...Ch. 12 - Prob. 22PCh. 12 - Prob. 23PCh. 12 - Prob. 24PCh. 12 - Prob. 25PCh. 12 - Prob. 26PCh. 12 - Prob. 27PCh. 12 - Prob. 28PCh. 12 - The angular position of a pendulum is represented...Ch. 12 - A small object is attached to the end of a string...Ch. 12 - A very light rigid rod of length 0.500 m extends...Ch. 12 - A particle of mass m slides without friction...Ch. 12 - Review. A simple pendulum is 5.00 m long. What is...Ch. 12 - Prob. 34PCh. 12 - Prob. 35PCh. 12 - Show that the time rate of change of mechanical...Ch. 12 - Prob. 37PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - Prob. 41PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - Four people, each with a mass of 72.4 kg, are in a...Ch. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - Prob. 55PCh. 12 - A block of mass m is connected to two springs of...Ch. 12 - Review. One end of a light spring with force...Ch. 12 - Prob. 58PCh. 12 - A small ball of mass M is attached to the end of a...Ch. 12 - Prob. 60PCh. 12 - Prob. 61PCh. 12 - Prob. 62PCh. 12 - Prob. 63PCh. 12 - A smaller disk of radius r and mass m is attached...Ch. 12 - A pendulum of length L and mass M has a spring of...Ch. 12 - Consider the damped oscillator illustrated in...Ch. 12 - An object of mass m1 = 9.00 kg is in equilibrium...Ch. 12 - Prob. 68PCh. 12 - A block of mass M is connected to a spring of mass...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Assume that a pendulum used to drive a grandfather clock has a length L0=1.00 m and a mass M at temperature T=20.00 °C. It can be modeled as a physical pendulum as a rod oscillating around one end. By what percentage will the period change if the temperature increases by 10°C? Assume the length of the rod changes linearly with temperature, where L=L0(1+T) and the rod is made of (=18106C1) .arrow_forwardWe do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.arrow_forwardC, N A uniform plank of length L and mass M is balanced on a fixed, semicircular bowl of radius R (Fig. P16.19). If the plank is tilted slightly from its equilibrium position and released, will it execute simple harmonic motion? If so, obtain the period of its oscillation.arrow_forward
- Consider a particle of mass m attached to two idenfical springs YA ZILLII|////. each of length 1 and spring constant k (see the figure). The equilibrium configuration is the one wheie the springs are unstretched. There are no other external 1orces on the system. lr the particle is given a small displacement along the x-axis, which of the following describes the equation of mouon for small oscillations? lllarrow_forwardEx. 70 A particle performs S.H.M. of amplitude 10 V2 cm. Find at what distance from the mean position the potential energy will be equal to its kinetic energy.arrow_forwardQl: (Section A) Considering single degree undamped vibration system and Newton's equation as follow: më +kx=0; find the solution of the displacement equation [(t)=Cietwnt+C2e¬i®n'] for the case with: Wn = 2 rad/s, x (0) = 1 mm, and x(0) = V5 mm/s. (Section B) Given the matrix equation of motion of a two degree-of-freedom system 2k -k ||x, = 0 -k 4k ||x2 Зт as: m ||*. Determine (a) the natural frequencies, (b) the modes shapes.arrow_forward
- A particle of unit mass moves along the x-axis under the influence of a potential, V(x)= x(x – 2). The particle is found to be in stable equilibrium at the point x= 2. The %3D - time period of oscillation of the particle is (b) л (c) 2 (d) 27arrow_forwardA physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? For solid sphere Icm = 2/5 mr2. Also, why is the distance of the center of mass of the system from the point of oscillation 3R/2?arrow_forwardA physical pendulum consists of a disk of radius R = 2 m, whose mass is homogeneously distributed and is equal to 6 kg, is suspended just at a point on its perimeter. The puck is displaced from its equilibrium position. until it forms an angle θ = π/16 with respect to the vertical and is then released. find: a) The period of the system. b) Make a graph of angular position v/s time where the amplitude, initial phase and system period.arrow_forward
- A particle of mass m is in a one-dimensional potential field, where its potential energy depends on the coordinate x as U(x) = U,(1 – cos(ax)), U, and a are some constants. Find the period of small oscillations of the particle near the equilibrium position. d U(x). Note: F(x) = dx oscillations are small→ small deviation from the equilibrium position!arrow_forwardThe figure depicts the displacement of an oscillator x[m], as a function of time t[s] 2 1 -1 -2 -3 0 0.5 1 1.5 Mass of the oscillator is 1.1 kg. What is the oscillator's amplitude (with more than 2 significant digits)? A = 30*10^-1 m 2 Your last answer was interpreted as follows: 30-10-¹ What is the oscillator's angular velocity (with more than 2 significant digits)? w = 9.4*10^0 rad 2.5 3 3.5 4 Your last answer was interpreted as follows: 9.4. 10⁰ Write the equation for oscillator's position in the following format: x = A sin (wt + 6)? Insert the answer as follows: x = (A)*sin((omega)*t + (phi)), where (A), (omega). (phi) are replaced with numerical values of amplitude, angular velocity and smallest positive phase angle rounded to one decimal after the decimal separator.arrow_forwardThe period of oscillation of a simple pendulum is assumed to depend upon its length 1, bob mass m, maximum displacement angle Omas and gravitational acceleration g. (a) (b) (c) Perform a dimensional analysis to establish how / varies with these parameters. If the period of oscillation for a given pendulum on earth is 3 s, what will it be (for the same amplitude oscillations) on the moon (g = 1.62 ms)? What other parameters do you think / might depend upon (weakly) in practice?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
SIMPLE HARMONIC MOTION (Physics Animation); Author: EarthPen;https://www.youtube.com/watch?v=XjkUcJkGd3Y;License: Standard YouTube License, CC-BY